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arXiv · 2011.10323

On the moments of the partition function of the C$\beta$E field

Theodoros Assiotis
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Abstract

We obtain a combinatorial formula for the positive integer moments of the partition function of the $C\beta E_{N}$ field, or equivalently the moments of the moments of the characteristic polynomial of the $C\beta E_{N}$ ensemble. We then use this formula to establish the large $N$ asymptotics of these moments in the "moment-supercritical" regime. A key role is played by Jack polynomials.

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Theodoros Assiotis. 2020-11-20. On the moments of the partition function of the C$\beta$E field. https://arxiv.org/abs/2011.10323

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